Role in The Statistical Definition of Entropy
Further information: Entropy (statistical thermodynamics)In statistical mechanics, the entropy S of an isolated system at thermodynamic equilibrium is defined as the natural logarithm of W, the number of distinct microscopic states available to the system given the macroscopic constraints (such as a fixed total energy E):
This equation, which relates the microscopic details, or microstates, of the system (via W) to its macroscopic state (via the entropy S), is the central idea of statistical mechanics. Such is its importance that it is inscribed on Boltzmann's tombstone.
The constant of proportionality k serves to make the statistical mechanical entropy equal to the classical thermodynamic entropy of Clausius:
One could choose instead a rescaled dimensionless entropy in microscopic terms such that
This is a rather more natural form; and this rescaled entropy exactly corresponds to Shannon's subsequent information entropy.
The characteristic energy kT is thus the heat required to increase the rescaled entropy by one nat.
Read more about this topic: Boltzmann Constant
Famous quotes containing the words role in the, role in, role, definition and/or entropy:
“Language makes it possible for a child to incorporate his parents’ verbal prohibitions, to make them part of himself....We don’t speak of a conscience yet in the child who is just acquiring language, but we can see very clearly how language plays an indispensable role in the formation of conscience. In fact, the moral achievement of man, the whole complex of factors that go into the organization of conscience is very largely based upon language.”
—Selma H. Fraiberg (20th century)
“So successful has been the camera’s role in beautifying the world that photographs, rather than the world, have become the standard of the beautiful.”
—Susan Sontag (b. 1933)
“A famous theatrical actress
Played best in the role of malefactress.
Yet her home-life was pure
Except, to be sure,
A scandal or two just for practice.”
—Anonymous.
“Although there is no universal agreement as to a definition of life, its biological manifestations are generally considered to be organization, metabolism, growth, irritability, adaptation, and reproduction.”
—The Columbia Encyclopedia, Fifth Edition, the first sentence of the article on “life” (based on wording in the First Edition, 1935)
“Just as the constant increase of entropy is the basic law of the universe, so it is the basic law of life to be ever more highly structured and to struggle against entropy.”
—Václav Havel (b. 1936)